Following [1]}, the CAViaR specification in (REF ) allows us to derive the VaR of an asset at level \(\tau _j\)  by estimating the corresponding quantile at the \(\tau _j\) -th level, through a conditional autoregressive structure. In the following, we consider several CAViaR formulations, depending on the choice of the NIC function \(\ell (\cdot )\) . We then extend the idea of [2]} to a multivariate setting, in order to model and estimate the ES component dynamically.
